A Survey of Numerical Methods for Shape from Shading

Several algorithms have been suggested for the shape from shading problem, and some years have passed since the publication of Horn and Brooks’ book [27]. In this survey paper, we try to update the approach in presenting some algorithms which seem to be particularly representative of three classes of methods: (i) methods based on partial differential equations, (ii) minimization methods, and (iii) methods approximating the image irradiance equation. One of the goals of this paper is to set the comparison of these methods on a firm basis. To this end, we provide a brief description of each method highlighting their basic assumptions and mathematical properties. We examine some numerical examples comparing the methods in terms of their efficiency and accuracy in the reconstruction of surfaces corresponding to synthetic as well as to real images. We also discuss their robustness faced with the presence of perturbations concerning the direction of the light source, and compare their accuracy in terms of a number of error indicators.

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